… In fact, we rigorise the entire “map” of the replica symmetric phase as predicted in [33,43,44], …
condensation phase transition does indeed separate a “replica symmetric” phase without …

… Charting the replica symmetric phase … We show that replica symmetry of the Boltzmann
distribution holds for … version are mutually contiguous in this phase. Moreover, we derive a cavity …

… the replica symmetry breaking phase transition at the Kesten-Stigum bound, thus charting the
replica symmetric phase for … The key feature of the replica-symmetric phase is that whp two …

… ‘replica symmetry’ in statistical mechanics [50,51], is known to occur: high temperature regions
in phase … Under this replica symmetric regime, ‘replica symmetric formulas’ can be proved …

… of replica symmetry, that is concentration of the overlap, induces strong replica symmetry, …
the model, and this in the whole phase diagram (an implication also exploited in the replica …

… 0 , 1 ) (independent of g ij ), replica symmetry has recently been shown in Ref. 13 for …
replica symmetry is to date only known above the AT line up to a bounded region in the (β, h)-phase …

… replica phase boundary will lower bound the one-replica and upper bound the higher-replica
phase … state-transfer protocol also shares exactly the same phase diagram as we chart out …

… of the clump phase. Moreover, we have found that in the glassy phase the replica symmetric
… consideration about replica symmetry breaking that the first-order transition from the clump …

… state points, during which we observe the replicas reaching a stationary state (equilibrating …
a reasonable bordering of the phases. Although the chart symmetry is obvious, we should …

… 10 depicts the EXIT charts of five decoding methods. We observe that replica shuffled BP with
four … Based on EXIT charts analysis, we derived an estimate for the least number of groups …